Trade induces many different types of reallocations across firms and products. These reallocations include selection effects (which products are sold where; which firms survive, and which ones export) as well as competition effects (responses in markups that generate changes in the relative sales of products in a given destination).

1. Competitive Effects of Trade: Theory and Measurement
ADEMU – Pierre Werner Chair Lecture
Marc J. Melitz
Harvard University
September 20, 2016

2. Starting Point: Selection and Competition Effects of Trade
In models with producer heterogeneity:
Trade induces many different reallocations across firms and products:
Selection effects (extensive margin):
Which products are sold where (across domestic and export
markets)
Which firms survive; which firms export (and where)
But also competition effects (intensive margin):
Conditional on selection (same products sold in a given market) –
trade affects the relative market shares of those products
These reallocations generate (endogenous) productivity changes that are
independent of “technology”
This endogenous productivity response, in turn, contributes to the
aggregate gains from trade
Handout p.1

3. Outline
Flexible theoretical framework to jointly capture selection and
competition effects from trade
Eschew more parametrized versions that aggregate nicely but obscure
specific transmission channels
Allows for generality in terms of trade scenarios considered:
Asymmetric liberalization
With and without balanced trade and factor price adjustments
... and adjustment path over time (short run versus long run)
In particular, will emphasize departures from CES preferences
benchmark: Variable Elasticity of Substitution (VES) preferences
Not just for sake of generality!
There is very strong (and mounting) empirical support for these
“departures”
Greatly sharpens predictions for impact of reallocations on aggregate
productivity
−→ New channel for competitive (intensive margin) effects of trade
Handout p.2

4. Outline (Cont.)
Examine the link between trade, reallocations and productivity
empirically
Use data on French multi-product firms to measure the reallocations
effects of trade within firms (across products)
−→ Highlight strong evidence for competitive effects stemming from
VES preferences
Directly measure productivity response of French firms to trade
Bottom line: Can explain 1% annual growth rate for French
manufacturing from 1995-2005
Connect back productivity gains to overall welfare gains from trade
(theoretically)
Handout p.3

5. VES Monopolistic Competition and Trade
Open economy version of Zhelodbodko et al (2012)
... along with long – and growing – literature on trade models with
endogenous markups
Additively separable preferences (nests CES) but most results using
residual demand curve can be extended to non-separable preferences
Handout p.4

6. VES Preferences and Demand
Demand for differentiated varieties xi is generated by Lc consumers who
solve:
max
xi ≥0
u(xi )di s.t. pi xi di = 1
satisfying (A1) u(xi ) ≥ 0; u(0) = 0; u (xi ) > 0; and u (xi ) < 0 for xi ≥ 0
(consumer expenditures on differentiated varieties normalized to 1)
This yields inverse demand (per consumer):
p(xi ; λ) =
u (xi )
λ
, where λ =
M
0
u (xi )xi di > 0
is the marginal utility of income (spent on differentiated varieties)
ρ(xi ; λ) ≡ [u (xi ) + u (xi )xi ] /λ is the associated marginal revenue
Let εp(xi ) ≡ −u (xi )xi /u (xi ) and ερ(xi ) ≡ −ρ (xi )xi /ρ(xi ) denote the
elasticities of inverse demand and marginal revenue (independent of λ)
Handout p.5

7. Firms and Production
Single factor of production: labor (wage normalized to 1)
Firm productivity ϕ (output per worker); same overhead labor cost f
Firms maximize profits
π(ϕ; λ) = max
xi ≥0
{Lc
[p(xi )xi − xi /ϕ] − f }
−→ Maximized quantity x(ϕ; λ) solves ρ(x; λ) = ϕ−1 (MR=MC)
so long as (A2) εp(x) < 1 and (A3) ερ(x) > 0 (MR positive and decreasing)
This leads to standard markup pricing
p(ϕ; λ) =
1
1 − εp(x (ϕ; λ))
ϕ−1
and firm size
q(ϕ; λ) = Lc
x(ϕ; λ) and r(ϕ; λ) = p(ϕ; λ)q(ϕ; λ)
Assume monopolistic competition: Firms take λ as outside their control
Handout p.6

8. Firms and Production (Cont.)
λ is a key endogenous market-level variable capturing the extent of
competition for a given level of market demand
Analogous to the CES price index
Increases in λ shift down/in the firms’ demand curves, and lowers the
firms’ optimal choice of price and quantity, and resulting profits
−→ Increased competition
Handout p.7

9. Shape of Demand
Assume that VES preferences fall in “price-decreasing” competition case
(Zhelobodko et al, 2012) −→ Demand becomes more elastic as move up
the demand curve
DMR
log 𝑝 , log 𝜌
log 𝑥
Consistent with vast majority of empirical evidence on firm markups and
pass-through:
Larger, better performing firms set higher markups
Incomplete pass-through of cost shocks to prices
Additional evidence on ‘more’ incomplete pass-through for
better-performing firms: Berman et al (2012) and Li et al (2015)
Handout p.8

10. Shape of Demand and Competition
D
Δ log 𝐿
Δλ
log 𝑝
log 𝑥
D
Δ log 𝐿
Δλ
log 𝑝
log 𝑥
Increases in competition (λ ) shift down εp(x) −→ more elastic
demand for all firms
Handout p.9

11. Implications for Competition and Firm Performance
log 𝜋%& , log 𝑟 , log 𝑞
log 𝜑
Δ log 𝐿
Δλ
Increases in competition (λ ) increase the elasticity of operating
profits, revenues, and output −→ intensive margin reallocations
Handout p.10

12. Closed Economy Equilibrium
Irreversible investment fE (in labor units) for firms to enter
Uncertain return: draw from a productivity distribution G(ϕ)
2 key equilibrium conditions:
Endogenous exit: Zero profit cutoff productivity such that
π(ϕ∗; λ) = 0. Firms with ϕ < ϕ∗ exit
Free entry:
∞
ϕ∗
π(ϕ; λ)dG(ϕ) = fE
These 2 equilibrium conditions jointly determine cutoff productivity ϕ∗
and competition level λ
Response of entry and wages depend on how model is closed:
Single sector (GE): Exogenous labor supply of workers Lw = Lc.
Wages adjust to ensure labor market equilibrium.
Multiple sectors (PE): Exogenous expenditures on given sector (Lc
consumers). Endogenous labor supply of workers at exogenous
economy-wide wage.
Handout p.11

13. Adjustment Path to Long Run Equilibrium
Re-establishing free-entry condition after a trade-shock may take time
Especially for downward response of entry!
In the short-run, the endogenous exit (zero-cutoff profit) condition would
still hold; but not the free-entry condition
Instead, the set of (potential) producers is fixed in the short-run
−→ Mass M of firms with productivity distribution G(ϕ)
Handout p.12

14. Opening Economy to Trade
Consider trade with destination F:
Exports to F:
Firms incur a per-unit trade cost τ and fixed export cost fX to reach F
Market size Lc
F and competition level λF determine export profits
πX (ϕ; λF )
Only firms with ϕ ≥ ϕ∗
X , such that πX (ϕ∗
X ; λ) = 0 export
(Zero cutoff profit condition for export market)
Free entry condition: same as in closed economy except that firms
anticipate profits
π(ϕ; λ, λF ) = 1[ϕ≥ϕ∗]πD(ϕ; λ) + 1[ϕ≥ϕ∗
X ]πX (ϕ; λF )
Same modeling setup in F (generating imports into domestic economy):
Mass MF of firms with productivity distribution GF (ϕ)
Firms incur trade costs τF , fF,X and earn profits πF,X (ϕ; λ)
Only firms with ϕ ≥ ϕ∗
F,X export
Handout p.13

15. Predictions for the Impact of Trade
Across all different types of trade liberalization scenarios:
Import and export trade liberalization
Single sector (GE) and multiple sector (PE)
Short run and long run
... Competition effect from liberalization (λ ) induces additional
intensive and extensive margin reallocations
Handout p.14

16. A Specific Example (Related to Empirical Results)
3 countries: destination D, France F, and W (ROW)
Demand shock in D: Lc
D
In order to focus on demand shocks and competition in D:
Assume that D is small relative to F and W
−→ Demand shocks in D do not affect country-wide equilibrium
variables in F or W (Apart from those related to exports to D)
Do not model any feedback loop from changes in exports from D
−→ Focus on equilibrium response in D
Handout p.15

17. Impact of Demand Shocks In Destination D
GE, PE, PE Short-Run trade scenarios all predict: Tougher competition
(λ ) in response to Lc
D
−→ intensive margin reallocations towards better performing products
−→ Positive extensive margin response for all exporters so long as fixed
export cost is high enough
log 𝜋%&
, log 𝑟 , log 𝑞
log 𝜑
Δ log 𝐿
Δλ
Handout p.16

18. Impact of Demand Shocks In Destination D: Productivity
Consequences for productivity:
Intensive margin effect unambiguously increases productivity
Extensive margin effect increases productivity – so long as new
exported products are more productive than firm average
Handout p.17

19. Measuring the Reallocation Effects of Trade Within Multi-Product Firms
Handout p.18

20. Why Within Multi-Product Firms?
It is very hard to measure the reallocation effects across firms at the
country/industry level:
Shocks that affect trade (institutions, technology, ...) are also likely to
affect the distribution of market shares across firms
Recent theoretical models of multi-product firms highlight how trade
induces a similar pattern of reallocations within firms as it does across
firms
Also fewer impediments to resource reallocation within firms
When measuring reallocations within multi-product firms, can:
Isolate trade shocks that are exogenous to individual firms –
controlling for country/industry effects
Control for firm-level technology changes
Look at same set of (narrowly defined products) sold by same firm
across destinations or time
Aside: Multi-product firms dominate world trade
Handout p.19

21. Similar Reallocations Across Firms and Within
Multi-Product Firms
Firms
Stable performance ranking for firms based on performance in any given
market (including domestic market) or worldwide sales
Better performing firms export to more destinations
Worse performing firms are most likely to exit (overall, or from any given
export market)
Products within Firms
Stable performance ranking across destinations (and for worldwide sales)
Better performing products are sold in more destinations
Worse performing products are most likely to be dropped from any given
market
Handout p.20

22. Data on French Multi-Product Exporters
Comprehensive customs data for firm-product exports to 229
destinations (d) for 1995-2005 (t)
Exclude service and wholesale/distribution firms (keep manufacturing
and agriculture)
Products recorded at 8-digit level (over 10,000 product codes)
Also country, sector (ISIC-3), and product (HS6) level trade for those
destinations:
GDP and other country level variables
Imports by destination (d) at ISIC3 (MI
d,t) and HS6 (Ms
d,t) level
Handout p.21

23. Competition Effects: Evidence Across Destinations
1101001000
MeanGlobalRatio
5 10 15
Destination GDP (log)
All countries (209)
AGO
ARE
ARG
AUS
AUT
BEL
BEN
BFA
BGD
BGR
BHR
BLR
BRACAN
CHECHL
CHN
CIV
CMR
COG COL
CRI
CYP
CZE
DEU
DJI
DNK
DOM
DZA
ECU
EGY
ESP
EST
FIN
GAB
GBR
GHA
GIN
GRC
GTM
HKG
HRV
HTI
HUN
IDN
IND
IRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KEN
KOR
KWT
LBN
LBY
LKA
LTU
LUX
LVA
MAR
MDG
MEX
MLIMLT
MRT
MUS
MYS
NER
NGA
NLD
NOR
NZL
OMN
PAK
PAN
PER
PHL
POL
PRT
QAT
ROM
RUS
SAU
SEN
SGPSVKSVN
SWE
SYR
TCD
TGO
THA
TUN
TUR
TWN
UKR
URY
USA
VEN
VNM
YEM
YUG
ZAF
1101001000
MeanGlobalRatio
6 8 10 12 14 16
Destination GDP (log)
Countries with more than 250 exporters (112)
Mean Global Sales Ratio and Destination Market Size
Handout p.22

24. Competition Effects: Evidence Across Destinations
1101001000
MeanGlobalRatio
12 14 16 18 20
Foreign Supply Potential (log)
All countries (209)
AGO
ANT
ARE
ARG
AUS
AUT
BEL
BEN
BFA
BGD
BGR
BHR
BLR
BRA CAN
CHECHL
CHN
CIV
CMR
COGCOL
CRI
CYP
CZE
DEU
DJI
DNK
DOM
DZA
ECU
EGY
ESP
EST
FIN
GAB
GBR
GHA
GIN
GRC
GTM
HKG
HRV
HTI
HUN
IDN
IND
IRL
IRN
ISL
ISR
ITA
JOR
JPN
KAZ
KEN
KOR
KWT
LBN
LBY
LKA
LTU
LVA
MAR
MDG
MEX
MLI MLT
MRT
MUS
MYS
NCL
NER
NGA
NLD
NOR
NZL
OMN
PAK
PAN
PER
PHL
POL
PRT
PYF
QAT
ROM
RUS
SAU
SEN
SGP
SPM
SVKSVN
SWE
SYR
TCD
TGO
THA
TUN
TUR
UKR
URY
USA
VEN
VNM
YEM
YUG
ZAF
1101001000
MeanGlobalRatio
12 14 16 18 20
Foreign Supply Potential (log)
Countries with more than 250 exporters (112)
Mean Global Sales Ratio and Foreign Supply Potential
Handout p.23

25. Reallocations Over Time: Measuring Trade Shocks
Changes in the destination markets over time also induce similar pattern
of reallocations
For all firms exporting to destination d, can measure change (growth
rate) in
˜∆GDPd,t
Total imports into d (in ISIC I) excluding French exports: ˜∆MI
d,t
Both capture demand shocks for French exporters to d
... but we can also construct a firm i-specific measure of the
trade-induced demand shock:
˜∆shockI
i,d,t ≡ ˜∆Ms
d,t ∀ products s ∈ I exported by firm i to d in t − 1
All 3 trade shocks strongly predict response (growth rate) of firm i’s
exports in a destination d along both intensive and extensive margins
Handout p.24

26. Impact of Trade Shocks on Reallocations Over Time
Destination-level over time:
Trade shock strongly predicts increased skewness of firm’s product mix
Theoretical connection with preferences satisfying previous evidence on
markups and pass-through
Aggregating up to firm-level:
Use (lagged) firm-destination export shares
Trade shocks strongly predict increased skewness of firm’s global product
mix (global exports and total production)
Handout p.25

27. Impact of Trade Shocks on Firm Productivity
Handout p.26

28. New Data and Productivity
Merge trade data with production data (comprehensive annual census)
Adds firm level variables (by year) for input and output use
Measure productivity as deflated value-added per worker
Aggregates (using firm labor shares) to welfare-relevant real
value-added per worker for French manufacturing:
Firm/product level:
ΦQ
i =
Yi /Pi
Li
ΦR
i =
Yi / ˜PS
Li
Sector/aggregate level:
ΦQ
S =
YS / ˜PS
LS
=
i∈S
Li
LS
ΦR
i
Handout p.27

29. Impact of Demand Shocks on Firm Productivity: Largest
French Exporters
Handout p.28

30. Counterfactual: Sector and Aggregate Productivity Effects
of Trade Shocks
Industry prod. trade shock % high exp.intens. % mfg. emp.
Radio, tv & communic. 1.8 4.94 59.77 4.31
Motor vehicles & trailers 1.62 9.8 52.39 7.82
Machinery 1.32 5.54 45.4 9.12
Chemicals 1.15 6.58 40.55 9.63
Fabricated metal .94 7.04 17.41 8.81
Medical & optical instrum. .85 5.84 46.82 3.53
Rubber and plastics .8 5.75 36.97 7.18
Electrical machinery .73 5.83 53.12 5.17
Basic metals .7 6.27 58.91 4.06
Food and beverages .66 6.2 14.12 11.88
Other transport equip. .65 7.25 69.14 4.3
Coke, refining & nuclear -.18 5.12 25.54 .93
Agg. Manufacturing 1.17 6.2 36.66 100
Note: Yearly averages based on 1995-2005 sample
Handout p.29

31. Endogenous Productivity Changes and Gains From Trade
Do productivity changes generated by reallocations contribute to
aggregate gains from trade?
Handout p.30

32. Endogenous Productivity Changes and Gains From Trade
Theoretical comparative static experiment: change the degree of firm
heterogeneity holding all other structural parameters constant
CES preferences case (Melitz & Redding, 2015):
Compare a heterogeneous firm model to a model with a degenerate
productivity distribution for exporters and non-exporters
−→ Welfare gains from trade liberalization are strictly higher in model
with endogenous selection (generated by the endogenous productivity
response)
Holds for general productivity distributions under firm heterogeneity
VES preferences case (Dhingra & Morrow, 2015):
Welfare effect is even stronger as intensive margin reallocations
towards higher productivity firms and lower average markups further
contribute to welfare gains
Handout p.31

33. Conclusion
Theory: Robust predictions for role of trade and competition in boosting
industrial productivity and gains from trade – especially when considering
more general VES preferences (relative to CES)
Within class of VES preferences featuring “price-decreasing”
competition
Demand shocks in export destinations induce French exporters to skew
their export sales towards their better performing products
−→ Strong evidence for competitive effects stemming from VES
preferences
−→ Substantial productivity response for French exporters most
impacted by those demand shocks
Handout p.32